The construction of a range restricted bivariate C^2 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. Sufficient conditions are derived on B?zier points in order to ensure that surfaces comprising quintic B?zier triangular patches are always positive and satisfy C^2 continuity conditions. The first and second derivatives at the data sites are then calculated (and modified if necessary) to ensure that these conditions are satisfied. Its construction is local and easily extended to include as upper and lower constraints to the interpolating surfaces of the form z = C(x,y) where C is a polynomial of degree less or equal to 5. A number of examples are presented.